Holy Crap. That stressed me out just reading it. There's no way I could deal with that for very long. Have you told your SO about what his dad is like with you? Is the father like this with his son or other family members? Is the father saying these things to you in front of other people or does he make sure it's when you and him alone? And he's being sneaky with these personal digs at you.
If it's in front of other people does anyone jump to your defense, eg. Your SO? Or do they all comply to the father's ways too. Do they all eat his food but you eat your healthy stuff?
The father is on a power trip and trying to control you for some reason. He Knows that it his house and you are not in a position to say much to complain or disagree with him. And he knows this big time.
I would not give in to any thing else he says if you can help it. Because it won't stop with the dog, which by the way that just ruffles my feathers, sorry your dog is being subjected to that. I do not give my dog people food either.
The father he'll just keep pushing you to see if you will comply or not or blow your top.
You are a grown woman. You can eat what the hell you want. And raise your dog the way you want. Your dog is like a child. Well my dog is my fur daughter. If it were a human child would you do something to harm your child because someone else said you need to do a b or c even though it was against your better judgement?
You know what's best for your dog.
Please don't let this man bully you because that's what he's doing. It's controlling. You need an advocate. Someone on your side. Your SO ought to be the one to defend you and stand up to his father on your behalf. He needs to say hey dad we really prefer to feed the dog this way. If you and SO are a "we" and intend to get your own place then it needs to be shown towards his father that you are united.

I have no clue what to advise other than hurry up and get on out of there. Is the financial gain worth it? Good luck.